and now of course this hexagon has gone back to a pentagon, or a pentagon-type object, five-sided, then to this quadrilateral that we see, finally going down to this triangle and a point. so it's a lot like the sphere case. >> greg, what i like so much about this discussion is that it's actually part of things that happen in the real world all the time. for example, when people are trying to image your body, they actually do it by constructing slices of you using some kind -- you know, like x-rays or whatever it is, and they rebuild your body from those slices. and the other way in which it's come up is in cubist art, in fact. and picasso's idea when he was creating this was actually inspired by discussions of how to see four-dimensional things as three-dimensional slices, which is how we're actually going to try to see four dimensions, like the flatlanders try to see three. >> absolutely. so it's easy to see how art and this would interact in the sense that your understanding here is very much so a metaphor in the same way that the art might be used. but let's look at it and see what w